### Parabolic inequalities with nonstandard growths and ${L}^{1}$ data.

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We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local

In this paper, a new a posteriori error estimator for nonconforming convection diffusion approximation problem, which relies on the small discrete problems solution in stars, has been established. It is equivalent to the energy error up to data oscillation without any saturation assumption nor comparison with residual estimator

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